Local and Global Existence of Mild Solution for Impulsive Fractional Stochastic Differential Equations

2014 ◽  
Vol 38 (2) ◽  
pp. 867-884 ◽  
Author(s):  
P. Balasubramaniam ◽  
N. Kumaresan ◽  
K. Ratnavelu ◽  
P. Tamilalagan
Keyword(s):  
Global Existence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Fractional Stochastic Differential Equations

An averaging principle for stochastic differential equations of fractional order 0 < α < 1

2020 ◽  
Vol 23 (3) ◽  
pp. 908-919 ◽  
Author(s):  
Wenjing Xu ◽  
Wei Xu ◽  
Kai Lu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Order ◽  
Mild Solution ◽  
Averaging Principle ◽  
Mean Square ◽  
Fractional Systems ◽  
Before And After ◽  
Fractional Stochastic Differential Equations ◽  
Fractional Equation

AbstractThis paper presents an averaging principle for fractional stochastic differential equations in ℝn with fractional order 0 < α < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.

scholarly journals Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 988
Author(s):  
Pengju Duan
Keyword(s):  
Brownian Motion ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Mild Solution ◽  
Intermittent Control

The paper is devoted to studying the exponential stability of a mild solution of stochastic differential equations driven by G-Brownian motion with an aperiodically intermittent control. The aperiodically intermittent control is added into the drift coefficients, when intermittent intervals and coefficients satisfy suitable conditions; by use of the G-Lyapunov function, the p-th exponential stability is obtained. Finally, an example is given to illustrate the availability of the obtained results.

scholarly journals Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Elhoussain Arhrrabi ◽  
M’hamed Elomari ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Stability Of Solutions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Existence And Stability ◽  
Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

Sign in / Sign up

Export Citation Format

Share Document